The board of adjustment shall consist of five members and whatever alternate members the mayor considers appropriate. One member, but not more than one, of the planning commission shall be a member of the board of adjustment. Another member shall be a member of the city council. The mayor, with the advice and consent of the city council, shall appoint and convene the board of adjustment when there is occasion to hear and decide variances in the terms of the zoning ordinance, or whenever the services of a land use authority are required.